The objective of this study was to simulate the lag time distribution of individual bacterial cells in a population
incubated under an isothermal condition. Spores of Clostridium sporogenes PA 3679 inoculated to ground
beef were incubated at 37 °C to develop a growth curve and determine its apparent lag time. The lag times of
individual cells were simulated using normal, lognormal, Gumbel, gamma, Weibull, and exponential distributions.
The growth process was modeled using the McKellar model. A 4th order Runge–Kutta method was
used to solve the McKellar model in conjunction with the Nelder–Mead method. The objective of the numerical
analysis was to search for the parameters in each lag time distribution model and the kinetic parameters
(specific growth rate and mean lag time) of the growth model such that a minimized residual sum of squared
errors (RSS) was found